Cellular pattern formation during Dictyostelium aggregation

The development of multicellularity in the life cycle of Dictyostelium discoideum provides a paradigm model system for biological pattern formation. Previously, mathematical models have shown how a collective pattern of cell communication by waves of the messenger molecule cyclic adenosine 3′5′-monophosphate (cAMP) arises from excitable local cAMP kinetics and cAMP diffusion. Here we derive a model of the actual cell aggregation process by considering the chemotactic cell response to cAMP and its interplay with the cAMP dynamics. Cell density, which previously has been treated as a spatially homogeneous parameter, is a crucial variable of the aggregation model. We find that the coupled dynamics of cell chemotaxis and cAMP reaction-diffusion lead to the break-up of the initially uniform cell layer and to the formation of the striking cell stream morphology which characterizes the aggregation process in situ. By a combination of stability analysis and two-dimensional simulations of the model equations, we show cell streaming to be the consequence of the growth of a small-amplitude pattern in cell density forced by the large-amplitude cAMP waves, thus representing a novel scenario of spatial patterning in a cell chemotaxis system. The instability mechanism is further analysed by means of an analytic caricature of the model, and the condition for chemotaxis-driven instability is found to be very similar to the one obtained for the standard (non-oscillatory) Keller-Segel system. The growing cell stream pattern feeds back into the cAMP dynamics, which can explain in some detail experimental observations on the time evolution of the cAMP wave pattern, and suggests the characterization of the Dictyostelium aggregation field as a self-organized excitable medium

Interplay of cell-cell signalling and multicellular morphogenesis during Dictyostelium aggregation

The cellular slime mould Dictyostelium discoideum provides a paradin model system for the study of multicellular pattern formation. Its life cycle involves a route to primitive multicellular organization which has independently evolved in terrestrial species of at least four groups of microorganisms (myxobacteria, acrasiomycota-the cellular slime moulds, myxomycota, and ciliata [1]). In these species a large number of single cells (nuclei in myxomycota) form through a process of aggregation and differentiation, a fruiting body

Turing patterns in fish skin?

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Dictyostelium discoideum: Cellular self-organisation in an excitable medium

The dynamics which govern the establishment of pattern and form in multicellular organisms remain a key problem of developmental biology. We study this question in the case of morphogenesis during aggregation of the slime mould Dictyostelium discoideum. Here detailed experimental information allows the formulation of a mechanistic model in which the central element is the coupling of the previously muchstudied intracellular cyclic AMP signalling with the chemotactic cell response in cyclic AMP gradients. Numerical simulations of the model show quantitatively how signal relay, chemotactic movement and adaptation orchestrate the collective modes of cell signalling and migration in the aggregating cell layer. The interaction of chemotaxis with the cyclic AMP excitation waves causes the initially homogeneous cell layer to become unstable towards the formation of a branching cell stream pattern with close cell-cell contacts as observed in situ. The evolving cell morphology in turn leads to a pattern of non-homogeneous excitability of the medium and thus feeds back into the cAMP dynamics. This feedback can expalin the decrease in signalling period and propagation speed with time, as well as observations on the structure of the spiral wave core in this self-organized excitable medium

A mathematical model for chemotactic movement and aggregation in cellular slime moulds

The cellular slime mould Dictyostelium discoideum (Dd)is a widely studied organism. In starvation conditions, Dd amoebae aggregate into a slug-like body which can crawl some distance before forming a fruiting body. The spores at the top of the body are scattered and amoebae emerge from them to feed in their new environment. Aggregation occurs in response to periodic waves of the chemoattractant cyclic adenosine 3'5'-monophosphate. (cAMP), emanating from the centre of the aggregation territory, which organize waves of cell movement towards the centre. To date, mathematical models focus on the dynamics of cAMP in homogeneous layer of stationary amoebae and, although they yield a valid description of the cAMP wave phenomena observed at the onset of aggregation, they do not consider cell movement

Global surfaces of section in the planar restricted 3-body problem

The restricted planar three-body problem has a rich history, yet many unanswered questions still remain. In the present paper we prove the existence of a global surface of section near the smaller body in a new range of energies and mass ratios for which the Hill's region still has three connected components. The approach relies on recent global methods in symplectic geometry and contrasts sharply with the perturbative methods used until now.Comment: 11 pages, 1 figur

Isotope effects in underdoped cuprate superconductors: a quantum phenomenon

We show that the unusual doping dependence of the isotope effects on transition temperature and zero temperature in - plane penetration depth naturally follows from the doping driven 3D-2D crossover, the 2D quantum superconductor to insulator transition (QSI) in the underdoped limit and the change of the relative doping concentration upon isotope substitution. Close to the QSI transition both, the isotope coefficient of transition temperature and penetration depth approach the coefficient of the relative dopant concentration, and its divergence sets the scale. These predictions are fully consistent with the experimental data and imply that close to the underdoped limit the unusual isotope effect on transition temperature and penetration depth uncovers critical phenomena associated with the quantum superconductor to insulator transition in two dimensions.Comment: 6 pages, 3 figure

Mathematical modelling of signalling in Dictyostelium discoideum

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Torque magnetometry on single-crystal high temperature superconductors near the critical temperature: a scaling approach

Angular-dependent magnetic torque measurements performed near the critical temperature on single crystals of HgBa_{2}CuO_{4+y}, La_{2-x}Sr{x}CuO_{4}, and YBa_{2}Cu_{3}O_{6.93} are scaled, following the 3D XY model, in order to determine the scaling function dG^{\pm}(z)/dz which describes the universal critical properties near T_{c}. A systematic shift of the scaling function with increasing effective mass anisotropy \gamma = (m_{ab}*/m_{c}*)^{1/2} is observed, which may be understood in terms of a 3D-2D crossover. Further evidence for a 3D-2D crossover is found from temperature-dependent torque measurements carried out in different magnetic fields at different field orientations \delta, which show a quasi 2D "crossing region'' (M*,T*). The occurrence of this "crossing phenomenon'' is explained in a phenomenological way from the weak z dependence of the scaling function around a value z = z*. The "crossing'' temperature T* is found to be angular-dependent. Torque measurements above T_{c} reveal that fluctuations are strongly enhanced in the underdoped regime where the anisotropy is large, whereas they are less important in the overdoped regime.Comment: 9 pages, 10 figures, submitted to PR

Oxygen isotope effect on the in-plane penetration depth in underdoped La_{2-x}Sr_{x}CuO_{4} single crystals

We report measurements of the oxygen isotope effect (OIE) on the in-plane penetration depth \lambda_{ab}(0) in underdoped La_{2-x}Sr_{x}CuO_{4} single crystals. A highly sensitive magnetic torque sensor with a resolution of \Delta \tau ~ 10^{-12} Nm was used for the magnetic measurements on microcrystals with a mass of ~ 10 microg. The OIE on \lambda_{ab}^{-2}(0) is found to be -10(2)% for x = 0.080 and -8(1)% for x = 0.086. It arises mainly from the oxygen mass dependence of the in-plane effective mass m_{ab}*. The present results suggest that lattice vibrations are important for the occurrence of high temperature superconductivity.Comment: 4 pages, 3 figures, submitted to PR